Multivariate Tests of Mean-Variance Efficiency and Spanning With a Large Number of Assets and Time-Varying Covariances

We develop a finite-sample procedure to test the mean-variance efficiency and spanning hypotheses, without imposing any parametric assumptions on the distribution of model disturbances. In so doing, we provide an exact distribution-free method to test uniform linear restrictions in multivariate linear regression models. The framework allows for unknown forms of nonnormalities as well as time-varying conditional variances and covariances among the model disturbances. We derive exact bounds on the null distribution of joint F statistics to deal with the presence of nuisance parameters, and we show how to implement the resulting generalized nonparametric bounds tests with Monte Carlo resampling techniques. In sharp contrast to the usual tests that are not even computable when the number of test assets is too large, the power of the proposed test procedure potentially increases along both the time and cross-sectional dimensions.     

A method for consideration of conditional dependencies in the Fellegi and Sunter model of record linkage

An objective of Record Linkage is to link two data files by identifying common elements. A popular model for doing the separation is the probabilistic one from Fellegi and Sunter. To estimate the parameters needed for the model usually a mixture model is constructed and the EM algorithm is applied. For simplification, the assumption of conditional independence is often made. This assumption says that if several attributes of elements in the data are compared, then the results of the comparisons regarding the several attributes are independent within the mixture classes. A mixture model constructed with this assumption has been often used. Within this article a straightforward extension of the model is introduced which allows for conditional dependencies but is heavily dependent on the choice of the starting value. Therefore also an estimation procedure for the EM algorithm starting value is proposed. The two models are compared empirically in a simulation study based on telephone book entries. Particularly the effect of different starting values and conditional dependencies on the matching results is investigated.     

Kernel Estimation of the Spectral Density of Stationary Random Closed Sets

A non‐parametric kernel estimator of the spectral density of stationary random closed sets is studied. Conditions are derived under which this estimator is asymptotically unbiased and mean‐square consistent. For the planar Boolean model with isotropic compact and convex grains, an averaged version of the kernel estimator is compared with the theoretical spectral density.     

Confidence Intervals Following Group Sequential Tests in Clinical Trails with Multivariate Observations

Several authors ( e.g. Kim and DeMets, 1987a, Biometrics) have developed methods for estimation following group sequential tests in clinical trials when each patient has only one response. In many long-term clinical trials, the subjects enter the study sequentially and yield repeated measurements or other types of multivariate observations at successive follow-up visits. Typically, investigators want to compare a parameter of interest such as the slope over time in a repeated measures trial etc. In this article, we propose an exact confidence interval for these parameters in a repeated measures trial, and compare it with a naive confidence interval using Monte Carlo simulation. This method is illustrated with a real example for bone density measurements.     

Empirical Bayes approach to wavelet regression using ϵ-contaminated priors

We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, which is usually the case in the existing literature, we elicit the ?-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis. The type II maximum likelihood approach to prior selection is used by maximizing the predictive distribution for the data in the wavelet domain over a suitable subclass of the ?-contamination class of prior distributions. For the prior selected, the posterior mean yields a thresholding procedure which depends on one free prior parameter and it is level- and amplitude-dependent, thus allowing better adaptation in function estimation. We consider an automatic choice of the free prior parameter, guided by considerations on an exact risk analysis and on the shape of the thresholding rule, enabling the resulting estimator to be fully automated in practice. We also compute pointwise Bayesian credible intervals for the resulting function estimate using a simulation-based approach. We use several simulated examples to illustrate the performance of the proposed empirical Bayes term-by-term wavelet scheme, and we make comparisons with other classical and empirical Bayes term-by-term wavelet schemes. As a practical illustration, we present an application to a real-life data set that was collected in an atomic force microscopy study.     

Comparison of exact tests for association in unordered contingency tables using standard,mid-p,and randomized test versions

Pearson’s chi-square (Pe), likelihood ratio (LR), and Fisher (Fi)–Freeman–Halton test statistics are commonly used to test the association of an unordered r×c contingency table. Asymptotically, these test statistics follow a chi-square distribution. For small sample cases, the asymptotic chi-square approximations are unreliable. Therefore, the exact p-value is frequently computed conditional on the row- and column-sums. One drawback of the exact p-value is that it is conservative. Different adjustments have been suggested, such as Lancaster’s mid-p version and randomized tests. In this paper, we have considered 3×2, 2×3, and 3×3 tables and compared the exact power and significance level of these test’s standard, mid-p, and randomized versions. The mid-p and randomized test versions have approximately the same power and higher power than that of the standard test versions. The mid-p type-I error probability seldom exceeds the nominal level. For a given set of parameters, the power of Pe, LR, and Fi differs approximately the same way for standard, mid-p, and randomized test versions. Although there is no general ranking of these tests, in some situations, especially when averaged over the parameter space, Pe and Fi have the same power and slightly higher power than LR. When the sample sizes (i.e., the row sums) are equal, the differences are small, otherwise the observed differences can be 10% or more. In some cases, perhaps characterized by poorly balanced designs, LR has the highest power.     

A unified framework for analysis and comparison of randomized response surveys of binary characteristics

The randomized response (RR) procedures for estimating the proportion (π)$(\pi )$ of a population belonging to a sensitive or stigmatized group ask each respondent to report a response by randomly transforming his/her true attribute into one of several response categories. In this paper, we present a common framework for discussing various RR surveys of dichotomous populations with polychotomous responses. The unified approach is focused on the substantive issues relating to respondents’ privacy and statistical efficiency and is helpful for fair comparison of various procedures. We describe a general technique for constructing unbiased estimators of π$\pi$ based on arbitrary RR procedures, from unbiased estimators based on an open survey with the same sampling design. The technique works well for any sampling design p(s)$p(s)$ and also for variance estimation. We develop an approach for comparing RR procedures, taking both respondents’ protection and statistical efficiency into account. For any given RR procedure with three or more response categories, we present a method for designing an RR procedure with a binary response variable which provides the same respondents’ protection and at least as much statistical information. This result suggests that RR surveys of dichotomous populations should use only binary response variables.     

An Efficient Method to Generate Data and Compute Exact P-Values in Goodness-of-Fit Testing

In this article, we use a characterization of the set of sample counts that do not match with the null hypothesis of the test of goodness of fit. Two direct applications arise: first, to instantaneously generate data sets whose corresponding asymptotic P-values belong to a certain pre-defined range; and second, to compute exact P-values for this test in an efficient way. We present both issues before illustrating them by analyzing a couple of data sets. Method's efficiency is also assessed by means of simulations. We focus on Pearson's X ² statistic but the case of likelihood-ratio statistic is also discussed.     

Developments in Maximum Likelihood Unit Root Tests

The exact maximum likelihood estimate provides a test statistic for the unit root test that is more powerful than the usual least-squares approach. In this article, a new derivation is given for the asymptotic distribution of this test statistic that is simpler and more direct than the previous method. The response surface regression method is used to obtain a fast algorithm that computes accurate finite-sample critical values. This algorithm is available in the R package mleur that is available on CRAN. The empirical power of the new test is shown to be much better than the usual test not only in the normal case but also for innovations generated from an infinite variance stable distribution as well as for innovations generated from a GARCH(1,1) process.